I defend the claim that physicalism is not committed to the view that non-phenomenal macrophysical truths are a priori entailed by the conjunction of microphysical truths , basic indexical facts , and a 'that's all' claim . I do so by showing that Chalmers and Jackson's most popular and influential argument in support of the claim that PIT ⊃ M is a priori, where 'M' stands for any ordinary, non-phenomenal, macroscopic truth, falls short of establishing its conclusion. My objection to Chalmers and Jackson's argument takes the form of a nested dilemma. Let 'Conceptual Competence Principle ' stand for the following claim: for any complete microphysical description D of a world w, a subject who is in possession of and competent with a macrophysical concept C is capable of determining a priori the extension of C. Either Jackson and Chalmers accept CCP or not. If the latter, then they cannot demonstrate that the conditional PIT ⊃ M is a priori. If the former, then they have a choice: they can either cite reasons that support the principle or argue that the principle should be taken for granted since it is entailed by the very notion of conceptual competence. But both alternatives are problematic. In regard to the first horn of this latter dilemma, I show not only that there are no good reasons to support the principle, but that there are also reasons to reject it. In regard to the second horn, I show that it cannot be the case that CCP is part of the very notion of conceptual competence. The conceptual capacity expressed by CCP requires that certain bridge principles or conditionals, which link the microphysical level to the macroscopic level, are either implicitly or explicitly given to the subject. But, as I argue, Chalmers and Jackson have no way of accounting for these bridge principles or conditionals in a manner that does not trivialize their position